Mirror Mirror on the Wall: Asset Prices and Wall Street

Before I became a geometer and after I studied economics, I worked as a pricing actuary for a reinsurance firm. Insurance companies aggressively market their products and in the process accumulate more risk than they can stomach. They offload this risk to heavily-capitalized reinsurance firms whose entire business is to bear such tail risks and for which they get compensated in the form of ceded premium. The job of the pricing actuary is easy: Compute the expected loss and add on a risk premium for the value-at-risk. Value-at-risk is the largest loss you would have to bear, say, once in a hundred years. Reinsurance pricing is relatively straightforward because the underlying shocks are exogenous and independent of each other. Because you are insuring only against acts of God, the probabilities are relatively stable. It’s all quite tame.

Contrast that to the untamed gyrations of the market. In sharp contrast to the reinsurance industry, shocks to asset prices are endogenous and highly correlated. It is dramatically harder to price risky assets than bundles of insurance policies. Not coincidently it is also much more interesting.

For about a year now, my professional research has focused on asset pricing and macrofinance. I’ve written about financial cycles before. In this post, I’ll summarize my findings on asset pricing for the layperson. All the technical details can be found in my recent paper. I’m a strong believer in the notion that unless you can explain your ideas in plain English, either you don’t understand them yourself or you are peddling snake oil. So in what follows, I’ll try to explain in a clear and straightforward manner precisely what I have figured out.

My intellectual wanderings have convinced me that every single discipline is organized around a single powerful idea—a master key that unlocks the field. The master key that makes asset prices intelligible is systematic risk.

Modern finance began when the focus moved away from stocks to portfolios. The fundamental insight of modern finance is that investors are not compensated for holding idiosyncratic risk; they are compensated for holding only systematic risk. Idiosyncratic risk is the risk that a particular asset will lose value. Such risks are easily diversifiable. Simply by holding a portfolio with a large enough number of assets, an investor can reduce the threat posed by any particular asset to her balance sheet virtually down to zero. If there was any compensation for holding idiosyncratic risk, it would be immediately bid away by diversified investors for whom the risk is as good as nonexistent.

The defining feature of systematic risk is that it is hard to diversify away. For instance, if the market as a whole were to decline, you would feel the pain no matter how diversified a portfolio of stocks you hold. The Capital Asset Pricing Model says that that’s all there is to it: The only systematic risk is market risk. Things are not so simple, of course. The Capital Asset Pricing Model provides a rather poor explanation of asset prices.

More generally, an asset pricing model tells you what constitutes systematic risk. It is quite literally a list of risk factors. The sensitivity of a portfolio’s returns to a risk factor is called the portfolio’s factor beta. The expected return on a portfolio (in excess of the risk-free rate) is then simply the sum of the betas multiplied by the risk premiums on the factors. Your portfolio’s factor beta is your exposure to that risk for which your compensation is the risk premium on that factor. You earn exactly the risk premium on a factor if your portfolio’s beta for that factor is 1 and all other factor betas of your portfolio are 0.

The workhorse asset pricing model is that of Kenneth French and Eugene Fama from the 1990s. They have two risk factors besides market risk. The first is the difference between returns on stocks with low market capitalization and stocks with high market capitalization. That’s the size factor. The second is the difference between returns on stocks with high relative value and stocks with low relative value; where relative value is given by ratio of the book value of the firm (what they show on their accounts) and the market value of the firm. That’s the value factor.

This 3-factor model does well in explaining stock prices, as does Carhart’s 4-factor model; also from the 1990s. Carhart added a fourth factor, momentum, to the Fama-French 3-factor model. He builds on on the observation that stocks that perform well in a given month also do well in the following month. The momentum factor is simply the difference in the return on stocks with high prior returns and stocks with low prior returns.

These two workhorse models have been so successful that they have percolated down from academic journals to personal finance. If you have a bit of money in the bank or in your 401K, you have probably talked to an investment advisor. (The usual advice is to be aggressive if you have a long investment horizon, and play safe otherwise.) They often talk about high beta stocks (by which they mean high market beta), size stocks, value stocks, and momentum stocks. That’s all irrelevant. What matters are your portfolio’s factor betas, not the factor betas of the stocks! You should think of your portfolio not as a collection of stocks but as a bundle of factors.

The big problem with size, value, and momentum, is that it is not at all clear why they sport positive risk premiums. In other words, we do not have a theory to explain the empirical performance of these risk factors. They are, in fact, anomalies begging for explanation.

In recent years, a powerful new theory of asset prices has emerged from the wreckage of the financial crisis. It is this theory that attracted me away from my research on the geometry of black holes.

At the heart of the theory are giant Wall Street banks, referred to in the jargon as broker-dealers. These big banking firms are some of the largest financial institutions in the world. JPMorgan, for instance, has $2.5 trillion in assets.

As the financial crisis gathered pace in the fall of 2007, Tobias Adrian at the New York Fed (now at the IMF) and Hyun Song Shin at Princeton University (now at the Bank of International Settlements) started paying attention to broker-dealer leverage. What they found was striking.

Leverage is naturally countercyclical. When asset prices rise, equity rises faster than assets since liabilities are usually more or less fixed. Leverage therefore falls when assets are booming. Conversely, leverage rises when asset prices fall. This holds in the aggregate for households, non-financial companies, commercial banks, and pretty much every one else—except broker-dealers. Dealer leverage is procyclical. This is because dealers aggressively manage their balance sheets. When perceived risk is low, they increase their leverage and expand their balance sheets. When perceived risk is high, they deleverage and shrink.

In the years since that first breakthrough, the balance sheets of broker-dealers have been tied to the great mortgage credit boom, the shadow banking system, the transmission channel of monetary policy, the global transmission of US monetary policycross-border transmission of credit conditions, the yield curve and the business cycle (or more properly the business-financial cycle), and of course, asset prices.

This is quite simply the most profound revision of our picture of the global monetary, financial and economic system in decades. More on that another day. Let’s stick to the topic at hand.

What is absolutely clear is that an intermediary risk factor belongs in the pricing kernel (the vector of systematic risks). There is no disagreement that such a factor must be based on broker-dealer balance sheets (as opposed to the much broader set of financial intermediaries).

The big disagreement is on precisely what is the right measure to use as the risk factor. There are three competing groups of academics here. The first is the original group around Tobias Adrian, who argue that leverage is the right factor, that the risk posed to investors’ portfolios is that dealers could deleverage and therefore drive down asset prices. The second group, based around Zhiguo He at Chicago University, argue that the capital ratio (the reciprocal of leverage) of the holding companies that own broker-dealer firms is the right factor. This is because dealers can access internal capital markets inside their parent firms, and therefore don’t have to shed assets in bad times as long as they can ask their parents for money.

Both of these models are based on the observation that dealers are the marginal investors in asset markets. In effect, they replace the representative average investor who had hitherto played the starring role in asset pricing theory with broker-dealers. Basically, times are good when the marginal investor has high risk appetite (the marginal value of her wealth is low) and they are bad when she has low risk appetite (the marginal value of her wealth is high). Assets that do well in bad times ought to offer lower compensation to the investor than assets that do badly. The marginal value of her wealth therefore belongs in the pricing kernel.

The third group is a circle of one centered around yours truly. I argue that except for the interdealer markets—which are important as funding markets but not as markets for risky assets—both non-dealer risk arbitrageurs (basically all other big fish in the market) and dealers are simultaneously marginal investors. For the business of broker-dealers is to make markets. That is, dealers quote a two-sided market and absorb the resulting order flow on their own books. Importantly, dealers provide leverage to risk arbitrageurs by letting them trade on margin. Balance sheet capacity is the risk-bearing capacity of the dealers with system-wide implications. It goes up with both dealer equity and dealer leverage. When balance sheet capacity is plentiful, risk arbitrageurs can easily take risky leveraged positions to bid away excess returns. Conversely, when balance sheet capacity is scare, risk arbitrageurs cannot obtain all the leverage they want and therefore find it harder to bid away excess returns.

What this implies is that even if dealers were not marginal investors, their balance sheet capacity but not their leverage, still ought to belong in the pricing kernel. And if dealer leverage is tamed as it has by financial repression since the crisis, fluctuations in balance sheet capacity would still whipsaw asset markets. Balance sheet capacity is like the weather; it affects everyone. Of course, what matters is not the absolute size but the relative size of balance sheet capacity. I therefore define my intermediary risk factor to be the ratio of the total assets of the broker-dealer sector to the total assets of the household sector.

The first thing I show, of course, is that my intermediary risk factor is priced in the cross-section of expected stock excess returns. That is to say: Stocks with high intermediary factor betas have higher expected excess returns than stocks with low intermediary betas. Remarkably, a 2-factor model with my intermediary factor and market as risk factors explains half the cross-sectional variation in expected excess returns and sports a mean absolute pricing error of only 0.3 percent. The 4-factor Carhart model with market, size, value and momentum as risk factors, can explain a greater portion of the cross-sectional variation but it has a much higher mean absolute pricing error of 1.9 percent. (The mean absolute pricing error is a much more important measure than the percentage of variation explained.) In fact, I have shown that no benchmark multifactor model is competitive with my parsimonious intermediary model.


What I do next is to extract the time-variation of the premiums on the risk factors using a dynamic pricing model. First, behold the intermediary risk premium (see chart). What I love about this chart is the sheer intelligibility of the fluctuations. You can literally see the financial booms of the late-1990s and the mid-2000s when the premium gets extraordinarily compressed. The intermediary premium contains macroeconomic information: It predicts US recessions (the dark bands) and is manifestly correlated with the business-financial cycle. Indeed, I show in the paper that it is both contemporaneously correlated with, and predicts 1 quarter ahead, US GDP growth.


There is clearly an important cyclical component in the intermediary risk premium. I isolate it using a bandpass filter that assigns fluctuations to the frequency at which they appear. The visuals are compelling. The lows of the cyclical component of the intermediary premium line up nearly perfectly with US recessions.


None of the benchmark premiums share these properties. In fact, their confidence intervals almost always straddle the X axis, meaning that they are not even statistically distinguishable from zero.


Here’s the money shot. The intermediary premium dwarfs the premiums on the benchmark factors. It appears to be at least thrice as great in amplitude as the benchmark premiums.


Lastly, I show that a portfolio that tracks my intermediary risk factor has dramatically higher returns than benchmark factor portfolios. Over the past fifty years, the market portfolio has returned 6% above the risk-free rate. Size and value portfolios have done worse. The momentum portfolio has done better. It has returned 8% above the risk-free rate. Meanwhile, the intermediary portfolio has returned 12% above the risk-free rate. Yet, it has the lowest volatility! The Sharpe ratio (the ratio of a portfolio’s mean excess return to its volatility) of the intermediary portfolio is in a class of its own. It is twice as high as that of the momentum portfolio, thrice as high as that of market and value, and almost four times as high as that of the size portfolio. If there was ever going to be a compelling reason for investment professionals to start paying attention to balance sheet capacity, this is it.

Market Size Value Momentum Intermediary
Mean excess return (annual) 6.5% 3.2% 4.4% 8.4% 12.1%
Mean excess return (qtrly) 1.6% 0.8% 1.1% 2.1% 2.9%
Volatility 8.4% 5.6% 5.7% 7.6% 5.1%
Skewness -48.1% 23.5% 57.9% -64.5% -44.9%
Sharpe ratio 18.8% 14.4% 19.1% 27.0% 57.3%

The implications of my work for macrofinance and investment strategies are interesting. But what is really interesting is what this tells us about the nature of the modern financial and economic system.

You are welcome to read and comment on my research paper here


2 thoughts on “Mirror Mirror on the Wall: Asset Prices and Wall Street

    1. Thanks. Doesn’t quite work like that. The premium is the reward for exposure to contemporaneous fluctuations in balance sheet capacity. It can be systematically harvested. But the theory doesn’t allow you to predict, say next quarter, market returns or anything like that.


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